Influence of high-permeability discs in an axisymmetric model of the Cadarache dynamo experiment

Numerical simulations of the kinematic induction equation are performed on a model configuration of the Cadarache von-Kármán-sodium dynamo experiment. The effect of a localized axisymmetric distribution of relative permeability μr that represents soft iron material within the conducting fluid flow is investigated. The critical magnetic Reynolds number Rmc for dynamo action of the first non-axisymmetric mode roughly scales like Rmμr − Rmc ∞ ∝ μ−1/2 r , i.e. the threshold decreases as μr increases. This scaling law suggests a skin effect mechanism in the soft iron discs. More important with regard to the Cadarache dynamo experiment, we observe a purely toroidal axisymmetric mode localized in the high-permeability discs which becomes dominant for large μr. In this limit, the toroidal mode is close to the onset of dynamo action with a (negative) growth rate that is rather independent of the magnetic Reynolds number. We qualitatively explain this effect by paramagnetic pumping at the fluid/disc interface and propose a simplified model that quantitatively reproduces numerical results. The crucial role of 6 Author to whom any correspondence should be addressed. New Journal of Physics 14 (2012) 053005 1367-2630/12/053005+16$33.00 © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft